Line Search.

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Presentation on theme: "Line Search."— Presentation transcript:

2 Line SearchLine search techniques are in essence optimization algorithms for one-dimensional minimization problems.They are often regarded as the backbones of nonlinear optimization algorithms.Typically, these techniques search a bracketed interval.Often, unimodality is assumed.ax*bExhaustive search requires N = (b-a)/ + 1 calculations to search the above interval, where  is the resolution.

7 Newton's MethodsIf your function is differentiable, then you do not need to evaluate two points to determine the region to be discarded. Get the slope and the sign indicates which region to discard.Basic premise in Newton-Raphson method:Root finding of first derivative is equivalent to finding optimum(if function is differentiable).Method is sometimes referred to as a line search by curve fit because it approximates the real (unknown) objective function to be minimized.

8 Newton-Raphson MethodQuestion: How many iterations are necessary to solve an optimization problem with a quadratic objective function ?

9 False Position Method or Secant MethodSecond order information is expensive to calculate (for multi-variable problems).Thus, try to approximate second order derivative.\Replace y''(xk) in Newton Raphson withHence, Newton Raphson becomesMain advantage is no second derivative requirementQuestion: Why is this an advantage ?